How do I know the eCommerce void or refund 'went through' and ended up on the customer's credit card?

You can confirm the void or refund by logging into your Virtual Terminal.  You should have been provided login information by your gateway provider.  You can access your Virtual Terminal login page in Jackrabbit by pointing to Tools and clicking Credit Cards/Bank Accounts Settings.  Click on the Virtual Terminal button.  Learn more about eCommerce by going to ePayments in Jackrabbit (Credit Card & Bank Account Draft).